Are you preparing for bank PO? Well, then you must know that quantitative aptitude is one of the most important and toughest sections of the bank PO exam. This section deals with maths. And if you are not so good with mathematics then let me help you. Have you heard of this famous saying “Practice makes a man perfect”? Well, if yes then get ready to solve different numerical to ace this section.

In this article, we will deal with quadratic equations. This is an important part of the quantitative aptitude syllabus. So keep reading the article till the end.

## Quadratic Equation Questions for Bank PO

A quadratic equation is an equation of the type ax2+bx+C=0. Here X is unknown and a,b,c numbers. Also, remember a cannot be 0. The value of the x is the root or solution of the equation.

### Methods to Solve Quadratic Equations

#### Factorisation

Factorization is the popular and easiest method to solve quadratic equations. Let us understand it step by step with the help of an example.

Example 1: 8×2 + 15 = 26x

Step 1: write the equation in ax2+bx+c=0

Then, 8×2-26x+15=0

Step 2: factorize the left side into the product of two factors

8×2-20x-6x+15=0

Step 3: Use the zero product rule.

4x(2x-5) – 3(2x-5)=0

Step 4: Now we get two equations i.e. 4x-3=0 and 2x-5=0

Therefore the value of X can be either X=¾ or 5/2.

#### Solving by Formula

There is a general formula to solve quadratic equations.

Formula=

X= -b +/- √b2-4ac

2a

Example,

x2-4x+1=0

Let’s solve this using the formula i.e. X= -b +/- √b2-4ac

2a

Here a=1, b=-4 and c=1, hence we get,

-(-4)+/- √(-4)2-4(1)(1)

2(1)

After solving the above, the answer would be (2+ √3) (2-√3)

#### Quadratic Equation Questions for Bank PO

DIRECTION (Q. 1-5):- Solve the following equations and mark the correct option.

1. I. 3.5×2-11.5x+9=0
2. 8y2-18y+10=0

(A) x > y

(B) x ≥ y

(C) y > x

(D) y ≥ x

(E) x = y or no relation can be established

1. I. 30×2-33x-18=0
2. 2y2+10y+2=0

(A) x > y

(B) x ≥ y

(C) y > x

(D) y ≥ x

(E) x = y or no relation can be established

1. I. 13/2-29/2x+8=0
2. 2y2-22y+10=0

(A) x>y

(B) x≥y

(C) y>x

(D) y≥x

(E) x = y or no relation can be established

1. I. x=-13+26
2. 16(y-1)2=2304

(A) x > y

(B) x ≥ y

(C) y > x

(D) y ≥ x

(E) x = y or no relation can be established

1. I. 14x+22y=58
2. 11/2x+7/2y=12.5

(A) x > y

(B) x ≥ y

(C) y > x

(D) y ≥ x

(E) x = y or no relation can be established

DIRECTIONS (Q. 6-9):- In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answer:-

1. I) x – √144  = 0
2. II) y2 – 196 = 0

(A) x> y`

(B) x ≥ y

(C) x< y

(D) x ≤ y

(E) x = y or the relationship cannot be established

1. I) x2- 42 = 214
2. II) y – √196= 0

(A) x> y

(B) x ≥ y

(C) x< y

(D) x ≤ y

(E) x = y or the relationship cannot be established

1. I) x2 – 15x + 56 = 0
2. II) y2- 4y – 5 = 0

(A) x> y

(B) x ≥ y

(C) x< y

(D) x ≤ y

(E) x = y or the relationship cannot be established

1. I) x2 + 6x + 9 = 0
2. II) y2 + 4y + 4 = 0

(A) x> y

(B) x ≥ y

(C) x< y

(D) x ≤ y

(E) x = y or the relationship cannot be established

1. In the given question, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answer
2. I) x – 3 = 0
3. II) y2 – 10y + 24 = 0

(A) x> y

(B) x ≥ y

(C) x< y

(D) x ≤ y

(E) x = y or the relationship cannot be established

DIRECTION (Q.11-15):- In the following question two equations are given in variables x and y. You have to solve these equations and determine the relation between x and y.

1. I. 12×2+58x+70=0
2. 14y2-46-60=0

(A) x > y

(B) x < y

(C) x ≥ y

(D) x ≤ y

(E) x = y or relation cannot be established

1. I. 18×2+87x+105=0
2. 81y2-72y+15=0

(A) x > y

(B) x < y

(C) x ≥ y

(D) x ≤ y

(E) x = y or relation cannot be established

1. I

II.

(A) x > y

(B) x < y

(C) x ≤ y

(D) x ≥ y

(E) x = y or no relationship could be established

1. I. 7.5×2+40.5x+15=0
2. 4y2+22y+24=0

(A) x > y

(B) x < y

(C) x ≤ y

(D) x ≥ y

(E) x = y or no relationship could be established

1. I. 2×3-1070=1592
2. y3-358=642

(A) x > y

(B) x < y

(C) x ≤ y

(D) x ≥ y

(E) x = y or no relationship could be established

### Previous Year Questions: Bank PO

#### IBPS PO 2019

Directions (1-5): In the following two equations questions numbered (I) and (II) are given. You have to solve both equations and Give answer (a) If x > y (b) If x ≥ y (c) If y > x (d) If y ≥ x (e) If x = y or no relation can be established

Q1. I. x² – 7x + 12 = 0

1. y² – 8y + 12 = 0

Q2. I. 2x² + x – 28 = 0

1. 2y² – 23y + 56 = 0

Q3. I. 2x² – 7x – 60 = 0

1. 3y² + 13y + 4 = 0

Q4. I. x² – 17x – 84 = 0

1. y² + 4y – 117 = 0

Q5. I. x2 = 81

1. (y-9)2 = 0

Solution

#1. E

#2. D

#3. D

#4. E

#5. E

#6. D

#### IBPS PO 2018

Directions (6-11): In each of these questions, two equations (i) and (ii) are given, you have to solve both the equations and give answers accordingly.

Q6. (i) 2x² + 9x + 9 = 0

(ii) 15y² + 16y + 4 = 0

(a) x > y

(b) x < y

(c) x ≥ y

(d) x ≤ y

(e) x = y or no relation can be established between x & y.

Q7. (i) 2x³ = √256

(ii) 2y² – 9y + 10 = 0

(a) x = y or no relation can be established between x & y.

(b) x < y

(c) x ≤ y

(d) x ≥ y

(e) x > y

Q8. (i) 6x² – 11x + 4 = 0

(ii) 3y² – 5y + 2 = 0

(a) x ≤ y

(b) x < y

(c) x ≥ y

(d) x > y

(e) x = y or no relation can be established between x & y.

Q9. (i) 3x² + 11x + 10 = 0

(ii) 2y² + 11y + 14 = 0

(a) x ≥ y

(b) x ≤ y

(c) x > y

(d) x < y

(e) x = y or no relation can be established between x & y.

Q10. (i) 12x² + 11x + 2 = 0

(ii) 12y²+ 7y + 1 = 0

(a) x ≥ y

(b) x = y or no relation can be established between x & y.

(c) x < y

(d) x ≤ y

(e) x > y

Q11. (i) 21x² + 10x + 1 = 0

(ii) 24y²+ 26y + 5 = 0

(a) x ≤ y

(b) x = y or no relation can be established between x & y.

(c) x ≥ y

(d) x > y

(e) x < y

Solution

#1. B

#2. C

#3. E

#4. A

#5. B

#6. B

#### IBPS PO 2017

Directions (12-16): In the following questions two equations numbered (I) and (II) are given. You have to solve both equations and Give answer

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) If x = y or the relationship cannot be established

Q12. (i) x2-5x+6=0

(ii)3y2+3y-18=0

Q13. (i) x2-11x+30=0

(ii) y2+y-0=0

Q14. (i) 2×2+2x-4=0

(ii) y2-5y+4=0

Q15. (i) x2+6x-16=0

(ii) y2-6y+5=0

Q16. (i) x2-4=0

(ii) y2-9y+20=0

Solution

#12. B

#13. A

#14. D

#15. E

#16. C

#### IBPS PO 2016

Directions (17-21): In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answers.

(a) if x y>

(b) if x  ³y

(c) if x < y

(d) if x £y

(e) if x = y or relationship between x and y cannot be established

Q17. (i) 3×2-22x+7=0

(ii) y2-15y+56=0

Q18. (i) 2×2-17x+36=0

(ii) 2y2-19y+44=0

Q19. (i) x- √169=0

(ii) y2-169=0

Q20. (i) 3×2+20x+25=0

(ii) 3y2+14y+8=0

Q21. (i) 3×2+5x+2=0

(ii) 3y2+18y+24=0

Solution

#17. D

#18. E

#19. B

#20. E

#21. A

##### Conclusion

I hope this article gave you a clear insight into quadratic equations. Remember the only and only key to solving and mastering this question is by practice. Hence try to solve as many questions as you can before you give your exam. Also for more interesting articles and bank PO-related information, visit UPSC Pathshala.

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Summary Article Name
Quadratic Equation Questions for Bank PO: Practice Question and Methods to Solve
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Quadratic equation is one of the most important sections of the Bank PO. Around 5-6 questions come from it. Click to find different methods to solve them with practice questions.
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